Mathematics is an "artificial" deliberately constructed language, supported crucially by: (1) special alpha-numeric characters and usages; (2) extra-special non-alphanumeric symbols; (3) special written formats within a single line, such as superscripts and subscripts; (4) grouping along a line, including bracketing using round brackets, parentheses, and braces; and (5) the clever use of two or more lines at a time (as in fraction notation), and the set-theoretic and logical connectives. Also in important "non-verbal" ways this "language" depends crucially on spatial-textual formatting devices, and non-verbal images, including tables with rows and columns, pictures, diagrams, and graphs, and spatial-visual conventions. These include isometric diagrams, angle-notch markings to show equal angles at the base of an isosceles triangle, chevron or arrowhead markings to show pairs of parallel lines, line-notch markings to show pairs of equal-length sides, arrowheads showing directions on axes of graphs, or on vectors and compass bearings. This article discusses the conceptual complexities in mathematics language. In the formal context of mathematics instruction, mathematical words or symbols may not always be clear. When learning new words, symbols, visual conventions, operations and procedures in mathematics, students must learn to distinguish the new and specific mathematical meanings from any familiar, looser, everyday meanings that might be confused with its mathematical use. This article also discusses how the "square root" was derived.